The number 1590
1590 is a composite number with 16 divisors. Its prime factorisation is 2 × 3 × 5 × 53. Divisors (16): 1, 2, 3, 5, 6, 10, 15, 30, 53, 106, 159, 265, 318, 530, 795, 1590.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1590: a Harshad number: divisible by its digit sum 15.
- 2
1590 is composite. Its prime factorisation is
- 3
The divisors add up to 3888; without 1590 itself that is 2298, so 1590 is abundant (2298 is more than 1590). Euler's totient φ(1590) = 416 numbers up to 1590 share no factor with it.
- 4
The digits of 1590 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 104 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1590 = 2 \times 3 \times 5 \times 53 \]
1590 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 3888 |
| Euler totient φ(n) | 416 |
| Square | 2528100 |
| Cube | 4019679000 |
| Square root | 39.874804 |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 104 |
| Scientific notation | 1.59 × |
1590 in other forms
| Form | Value |
|---|---|
| In words | one thousand five hundred and ninety |
| Roman numerals | MDXC |
| Binary (base 2) | 11000110110 |
| Octal (base 8) | 3066 |
| Hexadecimal (base 16) | 636 |
| Base 3 | 2011220 |
| As time | 1590 seconds = 26 min 30 s |
Is 1590 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1590 ÷ 2 = 795) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1590 ÷ 3 = 530) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1590 ÷ 5 = 318) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1590 ÷ 6 = 265) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | No (remainder 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (1590 ÷ 10 = 159) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1590 a prime number?
No. 1590 = 2 × 3 × 5 × 53, so it is divisible by 2.
What are the factors of 1590?
1, 2, 3, 5, 6, 10, 15, 30, 53, 106, 159, 265, 318, 530, 795, 1590.
What is 1590 in binary?
11000110110 (hexadecimal 636, octal 3066).
What is the square root of 1590?
About 39.8748.
What is 1590 in Roman numerals?
MDXC.
Is 1590 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 1590?
1590 is a Harshad number: divisible by its digit sum 15.